Robert Ullman

Proton Magnetic Relaxation in Polyethylene Oxide Solutions

Proton magnetic relaxation times have been measured in solutions of polyethylene oxide. Molecular weight, temperature, and solution concentration have been systematically varied. Several low‐molecular‐weight oligomers have been studied as well as polymers which vary in molecular weight from 4 × 103 to 4 × 106. The results show that in dilute solution both T1 and T1 are independent of molecular weight. T1 decreases with increasing concentration for concentrations greater than 0.2 g per ml of polymer, but is independent of concentration for more dilute solutions. T2 is independent of concentration in the limit of low concentration, but decreases rapidly with increasing concentration. The concentration dependence of T2 is a sensitive function of molecular weight. The relaxation mechanism has been analyzed using a model of rotameric transitions and the molecular geometry calculated from the known crystal structure of the polymer. The most important term is that arising from a conformational change about the C...

Intrinsic Viscosity of Wormlike Polymer Chains

The intrinsic viscosity of wormlike polymer chains has been calculated using the Kirkwood–Riseman method. The chain statistics are taken from the Hermans and Ullman analysis of the Kratky–Porod model. Results are obtained for several degrees of chain extension for chains of varying molecular weight as a function of the degree of hydrodynamic interaction. The finite cross section of the chain is explicitly introduced in the model. The limiting results of the rigid rod and of the random coil are obtained at low and high degrees of chain coiling, respectively. Application of this model to DNA leads to a Kuhn statistical bond length of 1020 A. The model was also applied to flexible polyelectrolytes in solutions of low salt concentration and to cellulose nitrate. A method of using the tabulated results for estimates of the degree of coiling of other polymer systems is described.

Mathematical analysis of factors influencing the skin thickness of asymmetric reverse osmosis membranes

The formation of the dense surface skin of asymmetric reverse osmosis membranes is analyzed in terms of a composite process involving solvent diffusion and polymer relaxation. The analysis indicates that films with minimum skin thickness result from (i) rapid polymer relaxation; (ii) strongly concentration‐dependent solvent diffusion coefficients. The numerical results are discussed in terms of experimental variables. It indicates great difficulty in producing asymmetric films with extremely thin surface skins. The implications of this finding are discussed. Experimental NMR self‐diffusion studies of acetone in cellulose acetate are reported.

The Concentration Dependence of the Viscosity of Solutions of Macromolecules

The theory of the concentration dependence of the viscosities of solutions is developed for the dumbbell, rigid rod, and flexible chain macromolecules. Both the intramolecular hydrodynamic interactions between the monomer units of the same molecule and the intermolecular interactions between monomer units of different molecules are considered. The methods of Riseman and Kirkwood are applied throughout. The numerical result of the calculation for the dumbbell shaped molecule is compared with that obtained by Simha.

Nuclear Magnetic Relaxation of Polymer Solutions

A theory of nuclear magnetic relaxation of solutions of chain macromolecules is presented. The relaxation takes place because of the relative motion of segments of the polymer chain containing magnetic nuclei. The analysis is based on the Brownian motion of isolated polymer molecules using a model which has been applied previously for dynamic viscoelasticity and dielectric relaxation of polymer solutions.The relative motion of magnetic nuclei may be considered as arising from three sources: (a) the relative motion of pairs of atoms rigidly attached to a chain segment, (b) the relative motion of chain segments, and (c) the motion of atoms relative to a chain segment to which they are attached. Cases (a) and (b) are treated here.

Intrinsic Viscosity of Coiling Macromolecules

The intrinsic viscosity of coiling molecules has been calculated using the Kirkwood—Riseman adaptation of the Oseen approximation. Four different models of chain segment distribution were treated: (a) a Gaussian coil, (b) an excluded volume model of Kurata and Yamakawa, (c) a coil expansion model suggested by Peterlin and (d) an excluded volume model deduced from the machine computation of Wall and Erpenbeck. In all cases the partially free draining coil was treated. The mathematical solution of the problem has been carried out on an IBM 704 computer.

Rotatory Motion of Dipolar Molecules Constrained by a Steady Electric Field

In this paper a calculation has been carried out on the rotatory diffusion of dipolar rodlike molecules in the presence of an electric field. The time correlation method is used for calculations of dynamic susceptibilities. This calculation has been shown to be in good agreement with the dynamic dielectric studies of Block and Hayes. In addition, the decay of electric birefringence (Kerr effect) in the presence of an electric field has been shown to be extremely sensitive to the relative magnitudes of the steady state field and the initially applied sensing field.

Angular Velocity Correlation Functions and High‐Frequency Dielectric Relaxation

The angular velocity correlation function can be studied through measurements of dielectric relaxation and far‐infrared absorption. Relations between these quantities are described in this article, and the data of Davies, Pardoe, Chamberlain, and Gebbie are analyzed. Velocity correlation times are obtained for molecules in four simple liquids. Hubbard has obtained a theoretical expression linking the velocity correlation time, the orientation correlation time, and the molecular moment of inertia. This expression is experimentally verified for molecules in nonviscous liquids. Certain paradoxical predictions are found when this expression is applied to viscous liquids and solids. This article considers stochastic models for relaxation, in which the probability of molecular reorientation is modulated by fluctuations in the intermolecular environment. These stochastic models lead to orientation and velocity correlation functions that are consistent with experimental observations.

Numerical Solutions of Singular Fredholm Equations

A singular Fredholm equation of the second kind is solved numerically by a Fourier series analysis in which the singularity is removed naturally, and by a Gaussian quadrature procedure in which the singularity was eliminated by an approximation using the law of the mean. In addition, an analytic solution of an associated Fredholm equation of the first kind was used for comparison with the numerical results. Some properties of these numerical solutions are indicated, and a brief discussion of the errors is given.

Sedimentation and Diffusion of Wormlike Polymer Chains

Sedimentation and diffusion constants of wormlike polymer chains have been calculated using methods of Kirkwood and collaborators. The chain statistics are described according to Hermans and Ullman using the (Kratky–Porod) model. The results are obtained for several chain lengths at varying degrees of flexibility for several possible values of the segmental friction constant. Application of these calculations and an earlier calculation on intrinsic viscosity led to a Kratky–Porod persistence length of about 600 A for double‐stranded DNA.